Kurt Gödel Research Center

2003 seminar talk: Preserving non-null with transitive nep forcings

Talk held by Jakob Kellner (KGRC) at the KGRC seminar on 2003-04-01.

Abstract

I will introduce the definitions of Suslin ccc, Suslin proper and transitive nep, demonstrate that many of the usual "definable" forcings of sets of reals are Suslin+, and present an application of these notions, a simplified version of Shelah's "preserving a little implies preserving much": If I is an ideal generated by a Suslin ccc forcing (e.g. null or meager), and P is a transitive nep forcing, and (in V and every forcing extension) P forces that no old positive Borel-set becomes null, then P forces that no old positive set becomes null.